Question

A gaseous compound has the empirical formula \(\mathrm{NO}_{2}\). If its molar mass is approximately \(92 \mathrm{~g} / \mathrm{mol}\), what is its molecular formula?

Short answer

The molecular formula of the compound is \(N2O4\).

Step-by-step solution

Compute Molar Mass of The Empirical Formula

Calculate the molar mass of the empirical formula (NO2). The molar mass of Nitrogen (N) is approximately 14 g/mol, and that of Oxygen (O) is approximately 16 g/mol. Since there are two Oxygen atoms, the molar mass of O2 is \(2 \times 16 = 32 \, g/mol\). So, the molar mass of NO2 is \(14 + 32 = 46 \, g/mol\).

Compare Molar Masses

Next, compare the molar mass of the empirical formula with the molar mass of the compound. The given molar mass of the compound is 92 g/mol. Divide this by the molar mass of NO2 to determine the ratio. \(92 \div 46 = 2\). This ratio tells us that the molecular formula contains twice as many atoms as the empirical formula.

Determine the Molecular Formula

Since the molecular formula has twice as many atoms as the empirical formula, we have \(2 \times (NO2) = N2O4\).

Key concepts

Empirical Formula

An empirical formula represents the simplest whole number ratio of atoms present in a compound. It does not show the actual number of atoms, but rather the smallest ratio between them. This is crucial in chemistry as it provides insights into the proportion of elements in a chemical compound without detailing the precise number of each atom present. For example, the empirical formula for the compound nitrogen dioxide is \( \text{NO}_2 \), which indicates that for every one nitrogen atom, there are two oxygen atoms.
Finding an empirical formula involves identifying the lowest possible ratio of atoms in a molecule, which can be determined through methods like combustion analysis or other forms of quantitative chemical analysis. It gives the basic skeletal structure of a compound but not the total composition in a single molecule.

Molar Mass

The molar mass is a fundamental concept in chemistry, representing the mass of one mole of a substance. It plays a pivotal role in converting between the number of atoms and the mass of an element or compound. The unit for molar mass is grams per mole (\( \text{g/mol} \)).
To calculate the molar mass of a compound, you sum up the molar masses of each constituent atom in its molecular or empirical formula. For nitrogen dioxide (NO2), for instance, you would add the molar mass of nitrogen (14 g/mol) to twice the molar mass of oxygen (2 × 16 g/mol). This results in 46 g/mol for NO2. Understanding the molar mass helps in determining the molecular formula when given the empirical formula and allows for conversion between mass and moles in chemical reactions.

Chemical Compounds

Chemical compounds are substances formed when two or more elements are chemically bonded together. Each compound has a unique composition that determines its properties and reactions. These compounds can be categorized into organic or inorganic based on the presence of carbon atoms.
In chemical compounds, the arrangement and type of atoms define its molecular and empirical formulas. The molecular formula provides the exact number of each type of atom in a molecule, like \( \text{N}_2\text{O}_4 \) for dinitrogen tetroxide, whereas the empirical formula provides the simplest ratio. This distinction is important when determining chemical properties and the behavior of a compound in different conditions. Understanding these formulas aids in synthesizing new compounds and predicting the outcomes of chemical reactions.